Consider the Monopolistic Competition Model studied in class for the following parameter values: Fixed costs in labor units: F = 2, Marginal cost in labor units: c = 1/2 Utility Function Parameter 0c =1/2 . Notice that in this case the utility function is: 00 1/2 u(q1 , 12, __________ ) = Z q.- 1:] (1) Calculate the autarky equilibrium for a country that has 10 agents with 8 units of labor each (i.e., the labor endowment is L=80 and the number of consumers/agents is 10) . (2) Free trade between two identical countries (Home and Foreign) Calculate the free trade equilibrium when each country looks like the country in question (1). (3) Show that a consumer (from either country) is happier in free trade than he/she was in autarky (you need to compare the home consumer's utility level in both situations). (4) Growth in the foreign country. Assume now that the foreign country has now 20 agents and therefore labor endowment has doubled (i.e. the total labor endowment in foreign is 160). Everything else is unchanged and the two countries are trading freely. Show how this change affects the level of happiness of the consumer in the home country (you need to compare the utility level of the home consumer in free trade before and after the change)